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Finitary Polyadic Algebras from Cylindric Algebras

Miklós Ferenczi

Studia Logica 87 (1):1-11 (2007)

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On the complexity of axiomatizations of the class of representable quasi‐polyadic equality algebras.Tarek Sayed Ahmed - 2011 - Mathematical Logic Quarterly 57 (4):384-394.details Using games, as introduced by Hirsch and Hodkinson in algebraic logic, we give a recursive axiomatization of the class RQPEAα of representable quasi-polyadic equality algebras of any dimension α. Following Sain and Thompson in modifying Andréka’s methods of splitting, to adapt the quasi-polyadic equality case, we show that if Σ is a set of equations axiomatizing RPEAn for equation image and equation imageequation image, k′ < ω are natural numbers, then Σ contains infinitely equations in which − occurs, one of (...) Download Export citation Bookmark 1 citation
A note on substitutions in representable cylindric algebras.Tarek Sayed Ahmed - 2009 - Mathematical Logic Quarterly 55 (3):280-287.details We show that it is impossible to define a substitution operator for arbitrary representable cylindric algebras that agrees in its basic properties with the notion of substitutions introduced for dimension complemented algebras. Download Export citation Bookmark 2 citations
Neat embeddings as adjoint situations.Tarek Sayed-Ahmed - 2015 - Synthese 192 (7):1-37.details Looking at the operation of forming neat $\alpha $ -reducts as a functor, with $\alpha $ an infinite ordinal, we investigate when such a functor obtained by truncating $\omega $ dimensions, has a right adjoint. We show that the neat reduct functor for representable cylindric algebras does not have a right adjoint, while that of polyadic algebras is an equivalence. We relate this categorial result to several amalgamation properties for classes of representable algebras. We show that the variety of cylindric (...) Download Export citation Bookmark 1 citation
On the definition and the representability of quasi‐polyadic equality algebras.Miklós Ferenczi - 2016 - Mathematical Logic Quarterly 62 (1-2):9-15.details We show that the usual axiom system of quasi polyadic equality algebras is strongly redundant. Then, so called non‐commutative quasi‐polyadic equality algebras are introduced (), in which, among others, the commutativity of cylindrifications is dropped. As is known, quasi‐polyadic equality algebras are not representable in the classical sense, but we prove that algebras in are representable by quasi‐polyadic relativized set algebras, or more exactly by algebras in. Download Export citation Bookmark 1 citation

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